In the context of multiuser detection for the DS-CDMA uplink, out-of-cell interference is usually treated as Gaussian noise, possibly mitigated by overlaying a long random cell code on top of symbol spreading. Different cells use statistically independent long codes, thereby providing means for statistical out-of-cell interference suppression. When the total number of (in-cell plus out-of-cell) users is less than the spreading gain, subspace identification techniques are applicable. If the base station is equipped with multiple antennas, then completely blind identification is possible via three-dimensional low-rank decomposition. This works with more users than spreading and antennas, but a purely algebraic solution is missing. In this paper, we develop an algebraic solution under the premise that the codes of the in-cell users are known. The codes of out-of-cell users and all array steering vectors are unknown. In this pragmatic scenario, we show that in addition to algebraic solution, better identifiability is possible. Our approach yields the best known identifiability result for three-dimensional low-rank decomposition when one of the three component matrices is partially known, albeit noninvertible. Simulations show that the proposed identification algorithm remains close to the pertinent asymptotic (symbol-independent) Cramér-Rao bound, which is also derived herein.